To fill the above gap, recent work in machine learning focused on extending deep neural networks to complex numbers and spectral representations.
Trabelsi et al. propose deep complex networks, investigating the complex-value neural network structure [1]}. However, they mainly concentrate on the problems of initialization, normalization, and activation functions when extending real-valued operations directly into the complex-value domain. Their designs focus more on complex-value representations than spectral representations, and do not take the properties of spectral data into consideration.
Rippel et al. study spectral representations for convolutional neural networks [2]}. However, their study focuses on spectral parametrizing of standard CNNs, instead of designing operations customized for spectral data. In addition, their work treats input data fully from the frequency perspective instead of the time-frequency perspective.
Yao et al. propose a neural network that takes short-time Fourier transformed data as inputs [3]}. Yet their design uses traditional CNNs and RNNs, combining the real and imagery parts of complex-value inputs as additional features.
